Quantum Black Holes: A macroscopic window into the microstructure of gravity

The thermodynamic behavior of black holes is a precious clue in unravelling the microscopic structure of quantum gravity.High precision computations of quantum black hole entropy provide a new window into the fundamental microscopic theoryof gravity and its deviations from classical general relativity. Traditional methods of quantum field theory have proved to benot well-suited to perform these computations. Two breakthroughs in my recent work establish new ground for progress.On one front, a new method to sum up all perturbative quantum contributions to the entropy of a large class of black holeshas been developed. This gives rise to the first exactly solvable model of a quantum black hole. On a second front, a longstanding theoretical obstacle called the wall-crossing problem has been cleared in my recent work on the microscopicdescription of black holes in string theory. The newly-developed field of mock modular forms is shown to be the correctframework to address questions of exact black hole entropy. This makes a large class of microscopic models amenable toanalytic control, many of which were previously beyond reach.These developments open up a new line of research that I propose to pursue along two intersecting avenues. First, I aim toextend the computations of exact quantum black hole entropy towards models of realistic black holes. Second, I aim toadvance the theoretical understanding of quantum black holes by investigating the deeper origins of mock modularsymmetry. As a concrete application, I aim to establish that newfound group-theoretical structures called “moonshine”symmetries are physically realized in quantum black holes, thus opening up connections between two exciting fields ofresearch previously thought to be distinct. Together, the broad goal is to explain black hole microstructure throughsystematic computations of exact quantum entropy, and to investigate its consequences on the fundamental microscopictheory of gravity.